The ac doesn't MECHANICALLY have anything to do with the engine performance other than a horsepower draw to run the compressor. To restate it a different way, there is no reason the compressor should cause a miss in the engine. A couple people have stated they have had wiring issues. You said you checked the harness but did you do a voltage drop test on the wiring from the compressor to the pcm (or junction it plugs into)? An ecm reflash is probably not going to fix your problem because I don't think the ecm has anything to do with the ac compressor. If you don't know how to trace and check wiring either find a friend who knows how, or take it to a reputable shop. (I would avoid a dealership because it seems that dealerships only know how to plug in a computer and follow the instructions given to them by said computer.)
If I were a betting individual, I would put money on there being a short in the ground wire to the compressor.